230 ON THE TOTAL INTENSITY OF INTERFERING LIGHT.
A similar formula holds good for q, whence D2I= limit of
Let now
2?r (#' — x)
-----1_------i. = Q.U)
whence
^ , 7
dx = -=-— du,
A7T
and the limits of u are ultimately — oo aud + °o , since a ultimately vanishes. Hence
.. . f
imit Of J
du
A similar formula holds good for y, and we have, therefore,
if A be the whole area of the aperture or apertures. Now / ought to be equal to A, and, therefore,
D = b\.
CASE II. Aperture in front of a screen.
The formula for the illumination is given iu Airy's Tract, Art. 73. We have as before,
= limit of jjjjjj*****1 cos j^"^- [^ - & + 2/"J - f]
~ y>dx dy dx'dy'